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Magazine Chapter 1: Q 112. (page 77)
Acing the first test Here are the scores of Mrs. Liao鈥檚 students on their first statistics test:
(a) Make a boxplot of these data.
(b) Use the boxplot you created in part (a) to describe how the students did on Mrs. Liao鈥檚 first test.
Short Answer
Part (a)
Part (b) Students scored good marks.
Step by step solution
Part (a) Step 1. Given information.
The given data in the sorted form is:
43, 45, 72, 73, 78, 80, 81, 82, 82.5, 85, 85.5, 86, 86, 87.5, 87.5, 88, 88, 89, 91, 91, 92, 93, 93.5, 93.5, 94.5, 94.5, 95, 96, 98
Part (a) Step 2. Find the outliers in the distribution.
As the number of data, values is even, then the median is:
The median of data values below the median (or at 25% of the data) is the first quartile. The first quartile is 82 because there are 15 data values below the median.
The median of the data values above the median (or at 75% of the data) is the third quartile. The third quartile is 93 since there are 15 data values above the median.
Observations that are more than 1.5 times the IQR above the third quarter or below the first quarter are considered outliers.
From the data, we know that 43 and 45 are outliers.
Part (a) Step 3. Make a boxplot of these data.
An Xis used to represent outliers. The boxplot's whiskers are at the minimum and highest values. The box has a vertical line at the median and starts at the first quartile and finishes at the third quartile.
Part (b) Step 1. Explain how the students did on Mrs. Liao’s first test.
We all know that the first quartile represents median values below the median and there are 15 values that are below the median from it we can find the first quartile, which is 82.
Therefore, 25% of students scored below 82 or equal to 82, and the rest 75% of students scored more than 82.
This all represents that students performed very well in the first test taken by Mrs. Liao.
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